Question

8. The endpoints of ST are s(-3, 2) and t(5,8). Find the coordinates of the midpoint of ST. Then find ST. OA midpoint: (1,5); ST = 5 OB midpoint: (1, 4); ST = 10 с midpoint: (1, 5); ST = 10 midpoint: (2,5); ST = 10​

Answer 1

Answer:

The mid point of ST is (1,5) and ST = 10 units

Step-by-step explanation:

It is given that,

S(-3,2) and T(5,8). We need to find the coordinates of the midpoint of ST and also ST.

Let (x,y) be the mid point of ST. Using mid-point formula we get :

$(x,y)=(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})$

We have, x₁ = -3, x₂ = 5, y₁ = 2 and y₂ = 8

So,

$(x,y)=(\dfrac{-3+5}{2},\dfrac{2+8}{2})\\\\(x,y)=(1,5)$

(1,5) is the midpoint of ST.

Using distance formula to find ST as follows :

$ST=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\\ST=\sqrt{(5-(-3))^2+(8-2)^2} \\\\ST=10\ \text{units}$

Hence, the mid point of ST is (1,5) and ST = 10 units.